As a planet revolves around the sun, the distance from the sun, as a function of the angular position φ, is given by the function
r(φ) = α / [ 1+ε cos(φ−φ0) ].
Calculate the perihelion and aphelion distances where we know α=1.3 ε=0.073 and φ0= 5.0
r(φ) = α / [ 1+ε cos(φ−φ0) ].
Calculate the perihelion and aphelion distances where we know α=1.3 ε=0.073 and φ0= 5.0

Perihelion occurs when cos(φ−φ0) =1, this occurs when φ =5° since φ0= 5.0° and φ−φ0 =0°
Then r(φ) = α / [ 1+ε cos(φ−φ0) ] = α / [ 1+ε] = 1.3/(1 +0.073) = 1.212
Aphelion occurs when cos(φ−φ0) = 1, this occurs when 185°
Then r(φ) = α / [ 1+ε cos(φ−φ0) ] = α / [ 1ε]= 1.3/(10.073) = 1.402
Then r(φ) = α / [ 1+ε cos(φ−φ0) ] = α / [ 1+ε] = 1.3/(1 +0.073) = 1.212
Aphelion occurs when cos(φ−φ0) = 1, this occurs when 185°
Then r(φ) = α / [ 1+ε cos(φ−φ0) ] = α / [ 1ε]= 1.3/(10.073) = 1.402